Can we request to have the pride flag removed from the logo?

Sure, there are many different cultures and viewpoints in the world of Trek, but if someone wants to follow a faith, or exercise their innate differences, they usually do it with modesty, in private, or in sole company of others just like them. Odo is shy about his transformations and was always hesitant to shapeshift in public. Worf and Kira exercise their respective religions in the privacy of their own quarters or sanctuary. Data curbs his desire to quote time to the seconds place, and routinely attempts to fit in my adopting his crewmates' styles and mannerisms. Sisko keeps his African decorations in his own quarters and very rarely wore the garb when in someone else's company. Klingon "pride" celebrations were almost always strictly Klingon-only affairs.
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If you had a different viewpoint in Star Trek, you kept it to yourself, unless you were in command and could offer a solution to a problem based on your own outlook. Innate differences in the physical characteristics of the species were hard to hide, but you never saw anybody shoving those differences in people's faces (except when Laas decided to fog the entire promenade). During issues concerning the Prime Directive, which were often catalysts for drawing out the stronger emotions in the crew, it was always the Captain (and the Star Fleet rulebook, technically) who had the last say.
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Anyways, here's the TLDR: Pride flag is just that: a symbol of pride that was borne out of the warring communities of present-day Earth. It represents a divided world. United people don't need flags to broadcast their differences. A pride flag doesn't align with the visions of Gene Roddenberry or Starfleet. If you want to affix some sort of flag that embraces the spirit of Star Trek, you should perhaps design a world government flag which might represent a united world? Please remove the rainbow flag.